Two loudspeakers, a and b, are driven by the same amplifier and emit sinusoidal waves in phase. the frequency of the waves emitted by each speaker is 172 hz. you are 8.00 m from speaker a. take the speed of sound in air to be 344 m/s. what is the closest you can be to speaker b and be at a point of perfectly destructive interference?

7 m .

Explanation:

For destructive interference

Path difference = odd multiple of λ /2

Wave length of sound from each of  A and B.

= speed / frequency

λ = 334 / 172 = 2 m

λ/2 = 1 m

If I am  1 m away from B , the path difference will be

8 - 1 = 7 m  which is  odd multiple of 1 or λ /2

So path difference becomes odd multiple of  λ /2.

This is the condition of destructive interference.

So one meter is the closest distance which I can remain at so that i can hear destructive interference.

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